\chapter{Algebraic inequalities}

\section{Algebraic inequalities and feasile regions}

\begin{definition}
an \emph{algebraic inequality} is an inequality equation containing constants and variables connected by the 4 operations and integer exponentiation.
\end{definition}

- give examples of algebraic inequalities

\begin{example}
$6x+2 \leq 50$
$x^2-3x \leq 2x$
\end{example}

\section{Algebraic manipulation with inequalities}


\subsection{Relation to algebraic equalities}
$a \geq b \iff a=b+k$
$a \leq b \iff a=b-k$

\subsection{Basic manipulations}